Civil Engineering Reference
In-Depth Information
8.2.2
Concentrated top load; single-storey buildings
With single-storey buildings when the load is concentrated on top floor level, the
basic sway critical loads are obtained by combining formulae (3.30) and (8.3):
(8.10)
The combination of formulae (3.31) and (8.4) leads to the critical load of pure torsional
buckling as
(8.11)
In formulae (8.10) and (8.11)
ρ
*
is the mass density per unit area of the top floor,
defined by formula (3.68).
When the warping stiffness dominates over the Saint-Venant torsional stiffness
(i.e.
k
→
0), formula (8.11) simplifies to
(8.12)
Formulae (8.11) and (8.12) cannot be used in the special case when the warping stiffness
is zero. In such a case, the combination of (formulae (3.31a) and (8.4a) leads to
(8.13)
8.3 DEFORMATIONS
By making use of the stiffnesses defined by formulae (8.1) to (8.4), the deformations of
buildings subjected to horizontal load can be easily calculated. When the formulae for
the horizontal displacements are derived, however, an important aspect has to be
borne in mind. The theoretical formulae in
Chapter 5
yield the displacements in the
'arbitrary' directions
x
and
y
(normally parallel with the sides of the building for
rectangular layouts), but the formulae of the lateral stiffnesses defined by formulae
(8.1) and (8.3) are related to principal directions
X
and
Y
.
